LMFDB - Embedded newform 637.2.g.k.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.3
Root			$0.355143 - 0.615126i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.k.373.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.355143 - 0.615126i) q^{2} +2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(0.644857 + 1.11692i) q^{5} +(0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +O(q^{10})$	\(q+(0.355143 - 0.615126i) q^{2} +2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(0.644857 + 1.11692i) q^{5} +(0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +0.916066 q^{10} -2.40788 q^{11} +(1.80049 + 3.11853i) q^{12} +(1.25409 + 3.38042i) q^{13} +(1.55274 + 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(-1.95169 - 3.38042i) q^{17} +(0.993655 - 1.72106i) q^{18} -5.89068 q^{19} +(-0.964379 + 1.67035i) q^{20} +(-0.855143 + 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} +5.97829 q^{24} +(1.66832 - 2.88961i) q^{25} +(2.52477 + 0.429109i) q^{26} -0.486640 q^{27} +(-2.80683 - 4.86157i) q^{29} +2.20578 q^{30} +(-1.10289 + 1.91026i) q^{31} +(2.91873 + 5.05540i) q^{32} -5.79790 q^{33} -2.77252 q^{34} +(2.09212 + 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} +(-2.09204 + 3.62351i) q^{38} +(3.01971 + 8.13966i) q^{39} +(1.60105 + 2.77310i) q^{40} +(3.89260 + 6.74219i) q^{41} +(-0.144857 + 0.250899i) q^{43} +(-1.80049 - 3.11853i) q^{44} +(1.80424 + 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} +(-0.638511 - 1.10593i) q^{47} +(-1.47782 + 2.55966i) q^{48} +(-1.18499 - 2.05245i) q^{50} +(-4.69943 - 8.13966i) q^{51} +(-3.44036 + 4.15192i) q^{52} +(6.81126 - 11.7974i) q^{53} +(-0.172827 + 0.299345i) q^{54} +(-1.55274 - 2.68942i) q^{55} -14.1841 q^{57} -3.98731 q^{58} +(2.01528 + 3.49057i) q^{59} +(-2.32211 + 4.02201i) q^{60} -4.60097 q^{61} +(0.783368 + 1.35683i) q^{62} +1.69131 q^{64} +(-2.96697 + 3.58061i) q^{65} +(-2.05908 + 3.56644i) q^{66} +7.57559 q^{67} +(2.91873 - 5.05540i) q^{68} +(7.61366 - 13.1872i) q^{69} +(-3.61366 + 6.25905i) q^{71} +6.94662 q^{72} +(7.50626 - 13.0012i) q^{73} +(-1.81768 - 3.14832i) q^{74} +(4.01712 - 6.95785i) q^{75} +(-4.40474 - 7.62923i) q^{76} +(6.07935 + 1.03324i) q^{78} +(4.65379 + 8.06060i) q^{79} -1.58310 q^{80} -9.56546 q^{81} +5.52973 q^{82} -1.36463 q^{83} +(2.51712 - 4.35978i) q^{85} +(0.102890 + 0.178210i) q^{86} +(-6.75852 - 11.7061i) q^{87} -5.97829 q^{88} +(0.449849 - 0.779162i) q^{89} +2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} -0.907052 q^{94} +(-3.79865 - 6.57945i) q^{95} +(7.02797 + 12.1728i) q^{96} +(-7.83288 + 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9	$ 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9} - 22 q^{10} - 2 q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} - 19 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{22} + 2 q^{23} - 6 q^{24} - 5 q^{25} + 3 q^{26} - 52 q^{27} - q^{29} - 8 q^{30} + 4 q^{31} + 33 q^{32} - 38 q^{33} + 6 q^{34} + 34 q^{36} + 10 q^{37} + 23 q^{38} - 19 q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 34 q^{52} - 2 q^{53} - 5 q^{54} + 3 q^{55} - 34 q^{57} - 22 q^{58} + 8 q^{59} + 11 q^{60} + 16 q^{61} + 5 q^{62} + 28 q^{64} + 4 q^{65} - 6 q^{66} - 12 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} + 10 q^{72} + 8 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} + 14 q^{80} + 48 q^{81} - 28 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 6 q^{88} + q^{89} + 52 q^{90} + 24 q^{92} + 7 q^{93} + 66 q^{94} - 21 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9 - 22 * q^10 - 2 * q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 - 19 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 2 * q^20 - 5 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 + 3 * q^26 - 52 * q^27 - q^29 - 8 * q^30 + 4 * q^31 + 33 * q^32 - 38 * q^33 + 6 * q^34 + 34 * q^36 + 10 * q^37 + 23 * q^38 - 19 * q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 34 * q^52 - 2 * q^53 - 5 * q^54 + 3 * q^55 - 34 * q^57 - 22 * q^58 + 8 * q^59 + 11 * q^60 + 16 * q^61 + 5 * q^62 + 28 * q^64 + 4 * q^65 - 6 * q^66 - 12 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 + 10 * q^72 + 8 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 - q^78 + 26 * q^79 + 14 * q^80 + 48 * q^81 - 28 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 6 * q^88 + q^89 + 52 * q^90 + 24 * q^92 + 7 * q^93 + 66 * q^94 - 21 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	−0.712711	−	0.701457i	$-0.752533\pi$
$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	0.963836	+	0.266497i	$0.0858664\pi$
$3$	2.40788			1.39019			0.695096	−	0.718917i	$-0.255362\pi$
$3$	2.40788			1.39019			0.695096	+	0.718917i	$0.255362\pi$
$4$	0.747746	+	1.29513i	0.373873	+	0.647567i
$5$	0.644857	+	1.11692i	0.288389	+	0.499504i	0.973425	−	0.229005i	$-0.0735472\pi$
$5$	0.644857	+	1.11692i	0.288389	+	0.499504i	−0.685037	+	0.728509i	$0.740214\pi$
$6$	0.855143	−	1.48115i	0.349111	−	0.604678i
$7$		0			0
$7$		0			0
$8$	2.48280			0.877803
$9$	2.79790			0.932632
$10$	0.916066			0.289686
$11$	−2.40788			−0.726004			−0.363002	−	0.931788i	$-0.618248\pi$
$11$	−2.40788			−0.726004			−0.363002	+	0.931788i	$0.618248\pi$
$12$	1.80049	+	3.11853i	0.519755	+	0.900243i
$13$	1.25409	+	3.38042i	0.347823	+	0.937560i
$13$	1.25409	+	3.38042i	0.347823	+	0.937560i
$14$		0			0
$15$	1.55274	+	2.68942i	0.400915	+	0.694406i
$16$	−0.613742	+	1.06303i	−0.153436	+	0.265758i
$17$	−1.95169	−	3.38042i	−0.473354	−	0.819873i	0.526181	−	0.850373i	$-0.323623\pi$
$17$	−1.95169	−	3.38042i	−0.473354	−	0.819873i	−0.999535	+	0.0304998i	$0.990290\pi$
$18$	0.993655	−	1.72106i	0.234207	−	0.405658i
$19$	−5.89068			−1.35142			−0.675708	−	0.737170i	$-0.736162\pi$
$19$	−5.89068			−1.35142			−0.675708	+	0.737170i	$0.736162\pi$
$20$	−0.964379	+	1.67035i	−0.215642	+	0.373502i
$21$		0			0
$22$	−0.855143	+	1.48115i	−0.182317	+	0.315783i
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	−0.321475	−	0.946918i	$-0.604179\pi$
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	0.980793	−	0.195053i	$-0.0624879\pi$
$24$	5.97829			1.22031
$25$	1.66832	−	2.88961i	0.333664	−	0.577923i
$26$	2.52477	+	0.429109i	0.495148	+	0.0841553i
$27$	−0.486640			−0.0936539
$28$		0			0
$29$	−2.80683	−	4.86157i	−0.521215	−	0.902772i	−0.999696	−	0.0246732i	$-0.992145\pi$
$29$	−2.80683	−	4.86157i	−0.521215	−	0.902772i	0.478480	−	0.878098i	$-0.341188\pi$
$30$	2.20578			0.402718
$31$	−1.10289	+	1.91026i	−0.198085	+	0.343093i	−0.947907	−	0.318546i	$-0.896805\pi$
$31$	−1.10289	+	1.91026i	−0.198085	+	0.343093i	0.749823	+	0.661639i	$0.230139\pi$
$32$	2.91873	+	5.05540i	0.515964	+	0.893676i
$33$	−5.79790			−1.00928
$34$	−2.77252			−0.475482
$35$		0			0
$36$	2.09212	+	3.62365i	0.348686	+	0.603942i
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	−0.575298	−	0.817944i	$-0.695114\pi$
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	0.996009	+	0.0892511i	$0.0284473\pi$
$38$	−2.09204	+	3.62351i	−0.339373	+	0.587812i
$39$	3.01971	+	8.13966i	0.483540	+	1.30339i
$40$	1.60105	+	2.77310i	0.253148	+	0.438466i
$41$	3.89260	+	6.74219i	0.607922	+	1.05295i	0.991582	+	0.129478i	$0.0413302\pi$
$41$	3.89260	+	6.74219i	0.607922	+	1.05295i	−0.383660	+	0.923474i	$0.625336\pi$
$42$		0			0
$43$	−0.144857	+	0.250899i	−0.0220904	+	0.0382618i	−0.876859	−	0.480747i	$-0.840366\pi$
$43$	−0.144857	+	0.250899i	−0.0220904	+	0.0382618i	0.854769	+	0.519009i	$0.173699\pi$
$44$	−1.80049	−	3.11853i	−0.271433	−	0.470136i
$45$	1.80424	+	3.12504i	0.268961	+	0.465853i
$46$	−2.24591	−	3.89003i	−0.331141	−	0.573553i
$47$	−0.638511	−	1.10593i	−0.0931364	−	0.161317i	0.815693	−	0.578485i	$-0.196356\pi$
$47$	−0.638511	−	1.10593i	−0.0931364	−	0.161317i	−0.908829	+	0.417168i	$0.863023\pi$
$48$	−1.47782	+	2.55966i	−0.213305	+	0.369455i
$49$		0			0
$50$	−1.18499	−	2.05245i	−0.167582	−	0.290261i
$51$	−4.69943	−	8.13966i	−0.658052	−	1.13978i
$52$	−3.44036	+	4.15192i	−0.477092	+	0.575767i
$53$	6.81126	−	11.7974i	0.935598	−	1.62050i	0.162034	−	0.986785i	$-0.448194\pi$
$53$	6.81126	−	11.7974i	0.935598	−	1.62050i	0.773564	−	0.633718i	$-0.218472\pi$
$54$	−0.172827	+	0.299345i	−0.0235188	+	0.0407357i
$55$	−1.55274	−	2.68942i	−0.209371	−	0.362642i
$56$		0			0
$57$	−14.1841			−1.87873
$58$	−3.98731			−0.523559
$59$	2.01528	+	3.49057i	0.262367	+	0.454433i	0.966870	−	0.255268i	$-0.0821636\pi$
$59$	2.01528	+	3.49057i	0.262367	+	0.454433i	−0.704503	+	0.709701i	$0.748830\pi$
$60$	−2.32211	+	4.02201i	−0.299783	+	0.519240i
$61$	−4.60097			−0.589094			−0.294547	−	0.955637i	$-0.595169\pi$
$61$	−4.60097			−0.589094			−0.294547	+	0.955637i	$0.595169\pi$
$62$	0.783368	+	1.35683i	0.0994878	+	0.172318i
$63$		0			0
$64$	1.69131			0.211413
$65$	−2.96697	+	3.58061i	−0.368007	+	0.444120i
$66$	−2.05908	+	3.56644i	−0.253456	+	0.438998i
$67$	7.57559			0.925505			0.462753	−	0.886487i	$-0.346862\pi$
$67$	7.57559			0.925505			0.462753	+	0.886487i	$0.346862\pi$
$68$	2.91873	−	5.05540i	0.353949	−	0.613057i
$69$	7.61366	−	13.1872i	0.916577	−	1.58756i
$70$		0			0
$71$	−3.61366	+	6.25905i	−0.428863	+	0.742812i	−0.996772	−	0.0802788i	$-0.974419\pi$
$71$	−3.61366	+	6.25905i	−0.428863	+	0.742812i	0.567910	+	0.823091i	$0.307752\pi$
$72$	6.94662			0.818668
$73$	7.50626	−	13.0012i	0.878542	−	1.52168i	0.0256006	−	0.999672i	$-0.491850\pi$
$73$	7.50626	−	13.0012i	0.878542	−	1.52168i	0.852941	−	0.522007i	$-0.174816\pi$
$74$	−1.81768	−	3.14832i	−0.211301	−	0.365985i
$75$	4.01712	−	6.95785i	0.463857	−	0.803424i
$76$	−4.40474	−	7.62923i	−0.505258	−	0.875133i
$77$		0			0
$78$	6.07935	+	1.03324i	0.688350	+	0.116992i
$79$	4.65379	+	8.06060i	0.523592	+	0.906889i	0.999623	+	0.0274598i	$0.00874182\pi$
$79$	4.65379	+	8.06060i	0.523592	+	0.906889i	−0.476031	+	0.879429i	$0.657925\pi$
$80$	−1.58310			−0.176996
$81$	−9.56546			−1.06283
$82$	5.52973			0.610656
$83$	−1.36463			−0.149788			−0.0748940	−	0.997192i	$-0.523862\pi$
$83$	−1.36463			−0.149788			−0.0748940	+	0.997192i	$0.523862\pi$
$84$		0			0
$85$	2.51712	−	4.35978i	0.273020	−	0.472884i
$86$	0.102890	+	0.178210i	0.0110949	+	0.0192169i
$87$	−6.75852	−	11.7061i	−0.724589	−	1.25503i
$88$	−5.97829			−0.637288
$89$	0.449849	−	0.779162i	0.0476839	−	0.0825910i	−0.841198	−	0.540727i	$-0.818149\pi$
$89$	0.449849	−	0.779162i	0.0476839	−	0.0825910i	0.888882	+	0.458136i	$0.151483\pi$
$90$	2.56306			0.270170
$91$		0			0
$92$	9.45742			0.986004
$93$	−2.65563	+	4.59968i	−0.275376	+	0.476965i
$94$	−0.907052			−0.0935553
$95$	−3.79865	−	6.57945i	−0.389733	−	0.675037i
$96$	7.02797	+	12.1728i	0.717289	+	1.24238i
$97$	−7.83288	+	13.5669i	−0.795309	+	1.37752i	0.127334	+	0.991860i	$0.459358\pi$
$97$	−7.83288	+	13.5669i	−0.795309	+	1.37752i	−0.922643	+	0.385655i	$0.873975\pi$
$98$		0			0
$99$	−6.73701			−0.677095
$100$	4.98992			0.498992
$101$	0.684905			0.0681506			0.0340753	−	0.999419i	$-0.489151\pi$
$101$	0.684905			0.0681506			0.0340753	+	0.999419i	$0.489151\pi$
$102$	−6.67589			−0.661012
$103$	−8.96246	−	15.5234i	−0.883097	−	1.52957i	−0.847879	−	0.530190i	$-0.822121\pi$
$103$	−8.96246	−	15.5234i	−0.883097	−	1.52957i	−0.0352185	−	0.999380i	$-0.511213\pi$
$104$	3.11366	+	8.39292i	0.305320	+	0.822993i
$105$		0			0
$106$	−4.83795	−	8.37957i	−0.469903	−	0.813895i
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	−0.994960	−	0.100268i	$-0.968030\pi$
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	0.584315	+	0.811527i	$0.301363\pi$
$108$	−0.363883	−	0.630264i	−0.0350147	−	0.0606472i
$109$	−6.04639	+	10.4727i	−0.579139	+	1.00310i	0.416439	+	0.909164i	$0.363278\pi$
$109$	−6.04639	+	10.4727i	−0.579139	+	1.00310i	−0.995578	+	0.0939352i	$0.970055\pi$
$110$	−2.20578			−0.210313
$111$	6.16197	−	10.6729i	0.584869	−	1.01302i
$112$		0			0
$113$	7.12635	−	12.3432i	0.670391	−	1.16115i	−0.307402	−	0.951580i	$-0.599460\pi$
$113$	7.12635	−	12.3432i	0.670391	−	1.16115i	0.977793	−	0.209571i	$-0.0672069\pi$
$114$	−5.03738	+	8.72500i	−0.471794	+	0.817171i
$115$	8.15608			0.760558
$116$	4.19760	−	7.27045i	0.389737	−	0.675044i
$117$	3.50882	+	9.45807i	0.324391	+	0.874399i
$118$	2.86285			0.263547
$119$		0			0
$120$	3.85514	+	6.67730i	0.351925	+	0.609552i
$121$	−5.20210			−0.472918
$122$	−1.63400	+	2.83018i	−0.147936	+	0.256232i
$123$	9.37293	+	16.2344i	0.845129	+	1.46381i
$124$	−3.29873			−0.296234
$125$	10.7519			0.961677
$126$		0			0
$127$	4.41231	+	7.64234i	0.391529	+	0.678148i	0.992651	−	0.121009i	$-0.0386129\pi$
$127$	4.41231	+	7.64234i	0.391529	+	0.678148i	−0.601122	+	0.799157i	$0.705280\pi$
$128$	−5.23681	+	9.07043i	−0.462873	+	0.801720i
$129$	−0.348798	+	0.604136i	−0.0307099	+	0.0531912i
$130$	1.14883	+	3.09669i	0.100759	+	0.271598i
$131$	9.71471	+	16.8264i	0.848778	+	1.47013i	0.882299	+	0.470689i	$0.155995\pi$
$131$	9.71471	+	16.8264i	0.848778	+	1.47013i	−0.0335206	+	0.999438i	$0.510672\pi$
$132$	−4.33536	−	7.50906i	−0.377344	−	0.653580i
$133$		0			0
$134$	2.69042	−	4.65994i	0.232417	−	0.402558i
$135$	−0.313813	−	0.543540i	−0.0270087	−	0.0467805i
$136$	−4.84565	−	8.39292i	−0.415511	−	0.719687i
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	0.560210	−	0.828351i	$-0.310720\pi$
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	−0.997478	+	0.0709806i	$0.977387\pi$
$138$	−5.40788	−	9.36673i	−0.460350	−	0.797349i
$139$	−4.07361	+	7.05571i	−0.345519	+	0.598457i	−0.985448	−	0.169977i	$-0.945631\pi$
$139$	−4.07361	+	7.05571i	−0.345519	+	0.598457i	0.639929	+	0.768434i	$0.278964\pi$
$140$		0			0
$141$	−1.53746	−	2.66296i	−0.129477	−	0.224262i
$142$	2.56674	+	4.44572i	0.215396	+	0.373076i
$143$	−3.01971	−	8.13966i	−0.252520	−	0.680672i
$144$	−1.71719	+	2.97426i	−0.143099	+	0.247855i
$145$	3.62001	−	6.27004i	0.300625	−	0.520698i
$146$	−5.33160	−	9.23460i	−0.441246	−	0.764261i
$147$		0			0
$148$	7.65419			0.629170
$149$	−9.78888			−0.801937			−0.400968	−	0.916092i	$-0.631326\pi$
$149$	−9.78888			−0.801937			−0.400968	+	0.916092i	$0.631326\pi$
$150$	−2.85330	−	4.94207i	−0.232971	−	0.403518i
$151$	−7.37034	+	12.7658i	−0.599790	+	1.03887i	0.393062	+	0.919512i	$0.371416\pi$
$151$	−7.37034	+	12.7658i	−0.599790	+	1.03887i	−0.992852	+	0.119355i	$0.961917\pi$
$152$	−14.6254			−1.18628
$153$	−5.46062	−	9.45807i	−0.441465	−	0.764640i
$154$		0			0
$155$	−2.84482			−0.228502
$156$	−8.28398	+	9.99733i	−0.663249	+	0.800427i
$157$	−10.2922	+	17.8266i	−0.821409	+	1.42272i	0.0832247	+	0.996531i	$0.473478\pi$
$157$	−10.2922	+	17.8266i	−0.821409	+	1.42272i	−0.904633	+	0.426191i	$0.859855\pi$
$158$	6.61105			0.525947
$159$	16.4007	−	28.4069i	1.30066	−	2.25281i
$160$	−3.76433	+	6.52001i	−0.297597	+	0.515452i
$161$		0			0
$162$	−3.39711	+	5.88397i	−0.266902	+	0.462288i
$163$	−3.98086			−0.311805			−0.155902	−	0.987772i	$-0.549829\pi$
$163$	−3.98086			−0.311805			−0.155902	+	0.987772i	$0.549829\pi$
$164$	−5.82136	+	10.0829i	−0.454572	+	0.787342i
$165$	−3.73881	−	6.47581i	−0.291066	−	0.504141i
$166$	−0.484640	+	0.839422i	−0.0376154	+	0.0651518i
$167$	−4.33923	−	7.51576i	−0.335780	−	0.581587i	0.647855	−	0.761764i	$-0.275666\pi$
$167$	−4.33923	−	7.51576i	−0.335780	−	0.581587i	−0.983634	+	0.180177i	$0.942333\pi$
$168$		0			0
$169$	−9.85451	+	8.47872i	−0.758039	+	0.652209i
$170$	−1.78787	−	3.09669i	−0.137124	−	0.237505i
$171$	−16.4815			−1.26037
$172$	−0.433264			−0.0330361
$173$	0.933934			0.0710057			0.0355028	−	0.999370i	$-0.488697\pi$
$173$	0.933934			0.0710057			0.0355028	+	0.999370i	$0.488697\pi$
$174$	−9.60097			−0.727848
$175$		0			0
$176$	1.47782	−	2.55966i	0.111395	−	0.192942i
$177$	4.85256	+	8.40487i	0.364740	+	0.631749i
$178$	−0.319522	−	0.553428i	−0.0239492	−	0.0414812i
$179$	13.5461			1.01248			0.506241	−	0.862392i	$-0.331034\pi$
$179$	13.5461			1.01248			0.506241	+	0.862392i	$0.331034\pi$
$180$	−2.69823	+	4.67348i	−0.201114	+	0.348340i
$181$	−8.86269			−0.658759			−0.329379	−	0.944198i	$-0.606839\pi$
$181$	−8.86269			−0.658759			−0.329379	+	0.944198i	$0.606839\pi$
$182$		0			0
$183$	−11.0786			−0.818953
$184$	7.85056	−	13.5976i	0.578751	−	1.00243i
$185$	6.60097			0.485313
$186$	1.88626	+	3.26709i	0.138307	+	0.239555i
$187$	4.69943	+	8.13966i	0.343657	+	0.595231i
$188$	0.954889	−	1.65392i	0.0696424	−	0.120624i
$189$		0			0
$190$	−5.39626			−0.391486
$191$	−15.3735			−1.11239			−0.556193	−	0.831053i	$-0.687739\pi$
$191$	−15.3735			−1.11239			−0.556193	+	0.831053i	$0.687739\pi$
$192$	4.07247			0.293905
$193$	−24.4953			−1.76321			−0.881606	−	0.471986i	$-0.843537\pi$
$193$	−24.4953			−1.76321			−0.881606	+	0.471986i	$0.843537\pi$
$194$	5.56359	+	9.63642i	0.399443	+	0.691855i
$195$	−7.14411	+	8.62170i	−0.511600	+	0.617413i
$196$		0			0
$197$	3.35706	+	5.81460i	0.239181	+	0.414273i	0.960479	−	0.278351i	$-0.0897878\pi$
$197$	3.35706	+	5.81460i	0.239181	+	0.414273i	−0.721299	+	0.692624i	$0.756454\pi$
$198$	−2.39260	+	4.14411i	−0.170035	+	0.294509i
$199$	2.43641	+	4.21998i	0.172712	+	0.299147i	0.939367	−	0.342913i	$-0.111414\pi$
$199$	2.43641	+	4.21998i	0.172712	+	0.299147i	−0.766655	+	0.642059i	$0.778080\pi$
$200$	4.14211	−	7.17434i	0.292891	−	0.507302i
$201$	18.2411			1.28663
$202$	0.243239	−	0.421303i	0.0171143	−	0.0296428i
$203$		0			0
$204$	7.02797	−	12.1728i	0.492056	−	0.852267i
$205$	−5.02034	+	8.69549i	−0.350636	+	0.607319i
$206$	−12.7318			−0.887069
$207$	8.84688	−	15.3232i	0.614901	−	1.06504i
$208$	−4.36319	−	0.741567i	−0.302533	−	0.0514184i
$209$	14.1841			0.981133
$210$		0			0
$211$	−1.84373	−	3.19344i	−0.126928	−	0.219846i	0.795557	−	0.605879i	$-0.207178\pi$
$211$	−1.84373	−	3.19344i	−0.126928	−	0.219846i	−0.922485	+	0.386033i	$0.873845\pi$
$212$	20.3724			1.39918
$213$	−8.70127	+	15.0710i	−0.596201	+	1.03265i
$214$	3.01712	+	5.22580i	0.206246	+	0.357228i
$215$	−0.373647			−0.0254825
$216$	−1.20823			−0.0822096
$217$		0			0
$218$	4.29467	+	7.43859i	0.290872	+	0.503805i
$219$	18.0742	−	31.3054i	1.22134	−	2.11543i
$220$	2.32211	−	4.02201i	0.156557	−	0.271164i
$221$	8.97966	−	10.8369i	0.604037	−	0.728968i
$222$	−4.37677	−	7.58078i	−0.293749	−	0.508789i
$223$	−4.40713	−	7.63338i	−0.295123	−	0.511169i	0.679890	−	0.733314i	$-0.262027\pi$
$223$	−4.40713	−	7.63338i	−0.295123	−	0.511169i	−0.975014	+	0.222145i	$0.928694\pi$
$224$		0			0
$225$	4.66779	−	8.08484i	0.311186	−	0.538990i
$226$	−5.06175	−	8.76721i	−0.336703	−	0.583186i
$227$	6.72557	+	11.6490i	0.446391	+	0.773173i	0.998148	−	0.0608325i	$-0.0193756\pi$
$227$	6.72557	+	11.6490i	0.446391	+	0.773173i	−0.551757	+	0.834005i	$0.686042\pi$
$228$	−10.6061	−	18.3703i	−0.702406	−	1.21660i
$229$	−3.40788	−	5.90263i	−0.225199	−	0.390056i	0.731180	−	0.682185i	$-0.238970\pi$
$229$	−3.40788	−	5.90263i	−0.225199	−	0.390056i	−0.956379	+	0.292128i	$0.905637\pi$
$230$	2.89658	−	5.01702i	0.190995	−	0.330812i
$231$		0			0
$232$	−6.96881	−	12.0703i	−0.457524	−	0.792456i
$233$	12.5336	+	21.7089i	0.821105	+	1.42220i	0.904860	+	0.425709i	$0.139975\pi$
$233$	12.5336	+	21.7089i	0.821105	+	1.42220i	−0.0837552	+	0.996486i	$0.526691\pi$
$234$	7.06404	+	1.20060i	0.461791	+	0.0784859i
$235$	0.823496	−	1.42634i	0.0537190	−	0.0930440i
$236$	−3.01384	+	5.22012i	−0.196184	+	0.339801i
$237$	11.2058	+	19.4090i	0.727894	+	1.26075i
$238$		0			0
$239$	−2.78521			−0.180160			−0.0900800	−	0.995935i	$-0.528712\pi$
$239$	−2.78521			−0.180160			−0.0900800	+	0.995935i	$0.528712\pi$
$240$	−3.81193			−0.246059
$241$	−3.48915	−	6.04338i	−0.224756	−	0.389288i	0.731490	−	0.681852i	$-0.238825\pi$
$241$	−3.48915	−	6.04338i	−0.224756	−	0.389288i	−0.956246	+	0.292563i	$0.905492\pi$
$242$	−1.84749	+	3.19995i	−0.118761	+	0.205701i
$243$	−21.5726			−1.38388
$244$	−3.44036	−	5.95888i	−0.220246	−	0.381478i
$245$		0			0
$246$	13.3149			0.848929
$247$	−7.38746	−	19.9130i	−0.470053	−	1.26703i
$248$	−2.73826	+	4.74280i	−0.173879	+	0.301168i
$249$	−3.28588			−0.208234
$250$	3.81846	−	6.61376i	0.241500	−	0.418291i
$251$	0.391515	−	0.678123i	0.0247122	−	0.0428028i	−0.853405	−	0.521249i	$-0.825466\pi$
$251$	0.391515	−	0.678123i	0.0247122	−	0.0428028i	0.878117	+	0.478446i	$0.158800\pi$
$252$		0			0
$253$	−7.61366	+	13.1872i	−0.478667	+	0.829075i
$254$	6.26801			0.393290
$255$	6.06092	−	10.4978i	0.379550	−	0.657399i
$256$	5.41095	+	9.37203i	0.338184	+	0.585752i
$257$	−1.62902	+	2.82155i	−0.101616	+	0.176003i	−0.912350	−	0.409410i	$-0.865734\pi$
$257$	−1.62902	+	2.82155i	−0.101616	+	0.176003i	0.810735	+	0.585414i	$0.199068\pi$
$258$	0.247746	+	0.429109i	0.0154240	+	0.0267152i
$259$		0			0
$260$	−6.85592	−	1.16523i	−0.425186	−	0.0722645i
$261$	−7.85322	−	13.6022i	−0.486102	−	0.841954i
$262$	13.8005			0.852595
$263$	29.5829			1.82416			0.912081	−	0.410010i	$-0.134475\pi$
$263$	29.5829			1.82416			0.912081	+	0.410010i	$0.134475\pi$
$264$	−14.3950			−0.885953
$265$	17.5691			1.07926
$266$		0			0
$267$	1.08318	−	1.87613i	0.0662898	−	0.114817i
$268$	5.66462	+	9.81141i	0.346022	+	0.599327i
$269$	−0.618249	−	1.07084i	−0.0376953	−	0.0652902i	0.846562	−	0.532290i	$-0.178668\pi$
$269$	−0.618249	−	1.07084i	−0.0376953	−	0.0652902i	−0.884258	+	0.467000i	$0.845335\pi$
$270$	−0.445794			−0.0271302
$271$	−12.6036	+	21.8300i	−0.765612	+	1.32608i	0.174311	+	0.984691i	$0.444230\pi$
$271$	−12.6036	+	21.8300i	−0.765612	+	1.32608i	−0.939923	+	0.341388i	$0.889103\pi$
$272$	4.79133			0.290517
$273$		0			0
$274$	−7.27062			−0.439234
$275$	−4.01712	+	6.95785i	−0.242241	+	0.419574i
$276$	22.7724			1.37073
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	0.686486	−	0.727143i	$-0.259152\pi$
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	−0.972967	+	0.230942i	$0.925819\pi$
$278$	2.89343	+	5.01157i	0.173537	+	0.300574i
$279$	−3.08577	+	5.34471i	−0.184740	+	0.319980i
$280$		0			0
$281$	9.56546			0.570628			0.285314	−	0.958434i	$-0.407902\pi$
$281$	9.56546			0.570628			0.285314	+	0.958434i	$0.407902\pi$
$282$	−2.18407			−0.130060
$283$	11.4320			0.679564			0.339782	−	0.940504i	$-0.389647\pi$
$283$	11.4320			0.679564			0.339782	+	0.940504i	$0.389647\pi$
$284$	−10.8084			−0.641361
$285$	−9.14670	−	15.8425i	−0.541803	−	0.938431i
$286$	−6.07935	−	1.03324i	−0.359479	−	0.0610971i
$287$		0			0
$288$	8.16632	+	14.1445i	0.481205	+	0.833472i
$289$	0.881831	−	1.52738i	0.0518724	−	0.0898457i
$290$	−2.57124	−	4.45352i	−0.150989	−	0.261520i
$291$	−18.8607	+	32.6676i	−1.10563	+	1.91501i
$292$	22.4511			1.31385
$293$	4.67781	−	8.10220i	0.273281	−	0.473336i	−0.696419	−	0.717635i	$-0.745225\pi$
$293$	4.67781	−	8.10220i	0.273281	−	0.473336i	0.969700	+	0.244299i	$0.0785579\pi$
$294$		0			0
$295$	−2.59913	+	4.50183i	−0.151327	+	0.262107i
$296$	6.35370	−	11.0049i	0.369301	−	0.639649i
$297$	1.17177			0.0679931
$298$	−3.47646	+	6.02140i	−0.201386	+	0.348810i
$299$	22.4790	+	3.82052i	1.29999	+	0.220947i
$300$	12.0151			0.693695
$301$		0			0
$302$	5.23506	+	9.06738i	0.301244	+	0.521769i
$303$	1.64917			0.0947423
$304$	3.61536	−	6.26199i	0.207355	−	0.359150i
$305$	−2.96697	−	5.13894i	−0.169888	−	0.294255i
$306$	−7.75721			−0.443450
$307$	8.11449			0.463119			0.231559	−	0.972821i	$-0.425617\pi$
$307$	8.11449			0.463119			0.231559	+	0.972821i	$0.425617\pi$
$308$		0			0
$309$	−21.5805	−	37.3786i	−1.22767	−	2.12639i
$310$	−1.01032	+	1.74993i	−0.0573823	+	0.0993891i
$311$	4.32008	−	7.48259i	0.244969	−	0.424299i	−0.717154	−	0.696915i	$-0.754556\pi$
$311$	4.32008	−	7.48259i	0.244969	−	0.424299i	0.962123	+	0.272616i	$0.0878888\pi$
$312$	7.49733	+	20.2092i	0.424453	+	1.14412i
$313$	2.61366	+	4.52700i	0.147733	+	0.255881i	0.930389	−	0.366573i	$-0.119469\pi$
$313$	2.61366	+	4.52700i	0.147733	+	0.255881i	−0.782656	+	0.622454i	$0.786136\pi$
$314$	7.31043	+	12.6620i	0.412551	+	0.714560i
$315$		0			0
$316$	−6.95971	+	12.0546i	−0.391514	+	0.678123i
$317$	−5.59646	−	9.69336i	−0.314329	−	0.544433i	0.664966	−	0.746874i	$-0.268446\pi$
$317$	−5.59646	−	9.69336i	−0.314329	−	0.544433i	−0.979295	+	0.202440i	$0.935113\pi$
$318$	−11.6492	−	20.1770i	−0.653255	−	1.13147i
$319$	6.75852	+	11.7061i	0.378404	+	0.655416i
$320$	1.09065	+	1.88906i	0.0609692	+	0.105602i
$321$	−10.2281	+	17.7155i	−0.570875	+	0.988785i
$322$		0			0
$323$	11.4968	+	19.9130i	0.639698	+	1.10799i
$324$	−7.15254	−	12.3886i	−0.397363	−	0.688254i
$325$	11.8603	+	2.01578i	0.657893	+	0.111815i
$326$	−1.41378	+	2.44873i	−0.0783018	+	0.135623i
$327$	−14.5590	+	25.2169i	−0.805115	+	1.39450i
$328$	9.66456	+	16.7395i	0.533636	+	0.924285i
$329$		0			0
$330$	−5.31126			−0.292375
$331$	20.0468			1.10187			0.550935	−	0.834548i	$-0.314271\pi$
$331$	20.0468			1.10187			0.550935	+	0.834548i	$0.314271\pi$
$332$	−1.02040	−	1.76738i	−0.0560017	−	0.0969978i
$333$	7.16006	−	12.4016i	0.392369	−	0.679602i
$334$	−6.16419			−0.337290
$335$	4.88517	+	8.46136i	0.266905	+	0.462294i
$336$		0			0
$337$	18.5866			1.01248			0.506239	−	0.862393i	$-0.331035\pi$
$337$	18.5866			1.01248			0.506239	+	0.862393i	$0.331035\pi$
$338$	1.71572	+	9.07293i	0.0933229	+	0.493502i
$339$	17.1594	−	29.7210i	0.931972	−	1.61422i
$340$	7.52866			0.408299
$341$	2.65563	−	4.59968i	0.143810	−	0.249087i
$342$	−5.85330	+	10.1382i	−0.316510	+	0.548212i
$343$		0			0
$344$	−0.359650	+	0.622933i	−0.0193911	+	0.0335863i
$345$	19.6389			1.05732
$346$	0.331680	−	0.574487i	0.0178312	−	0.0308846i
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	−0.992868	−	0.119220i	$-0.961961\pi$
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	0.393186	−	0.919459i	$-0.371373\pi$
$348$	10.1073	−	17.5064i	0.541809	−	0.938441i
$349$	−4.39316	−	7.60917i	−0.235160	−	0.407310i	0.724159	−	0.689633i	$-0.242228\pi$
$349$	−4.39316	−	7.60917i	−0.235160	−	0.407310i	−0.959319	+	0.282323i	$0.908895\pi$
$350$		0			0
$351$	−0.610291	−	1.64505i	−0.0325749	−	0.0878061i
$352$	−7.02797	−	12.1728i	−0.374592	−	0.648812i
$353$	7.71898			0.410840			0.205420	−	0.978674i	$-0.434144\pi$
$353$	7.71898			0.410840			0.205420	+	0.978674i	$0.434144\pi$
$354$	6.89341			0.366381
$355$	−9.32118			−0.494717
$356$	1.34549			0.0713110
$357$		0			0
$358$	4.81081	−	8.33256i	0.254259	−	0.440389i
$359$	5.29782	+	9.17609i	0.279608	+	0.484295i	0.971287	−	0.237909i	$-0.0764621\pi$
$359$	5.29782	+	9.17609i	0.279608	+	0.484295i	−0.691679	+	0.722205i	$0.743129\pi$
$360$	4.47958	+	7.75886i	0.236094	+	0.408928i
$361$	15.7002			0.826324
$362$	−3.14753	+	5.45167i	−0.165430	+	0.286534i
$363$	−12.5261			−0.657447
$364$		0			0
$365$	19.3619			1.01345
$366$	−3.93449	+	6.81474i	−0.205659	+	0.356212i
$367$	5.82067			0.303836			0.151918	−	0.988393i	$-0.451455\pi$
$367$	5.82067			0.303836			0.151918	+	0.988393i	$0.451455\pi$
$368$	3.88128	+	6.72257i	0.202325	+	0.350438i
$369$	10.8911	+	18.8639i	0.566968	+	0.982018i
$370$	2.34429	−	4.06043i	0.121874	−	0.211092i
$371$		0			0
$372$	−7.94295			−0.411823
$373$	26.0569			1.34917			0.674587	−	0.738195i	$-0.264322\pi$
$373$	26.0569			1.34917			0.674587	+	0.738195i	$0.264322\pi$
$374$	6.67589			0.345202
$375$	25.8893			1.33692
$376$	−1.58530	−	2.74581i	−0.0817554	−	0.141605i
$377$	12.9141	−	15.5851i	0.665112	−	0.802675i
$378$		0			0
$379$	−7.82662	−	13.5561i	−0.402026	−	0.696330i	0.591944	−	0.805979i	$-0.298361\pi$
$379$	−7.82662	−	13.5561i	−0.402026	−	0.696330i	−0.993970	+	0.109649i	$0.965027\pi$
$380$	5.68085	−	9.83952i	0.291421	−	0.504757i
$381$	10.6243	+	18.4019i	0.544300	+	0.942756i
$382$	−5.45979	+	9.45664i	−0.279347	+	0.483844i
$383$	−12.5588			−0.641724			−0.320862	−	0.947126i	$-0.603973\pi$
$383$	−12.5588			−0.641724			−0.320862	+	0.947126i	$0.603973\pi$
$384$	−12.6096	+	21.8405i	−0.643482	+	1.11454i
$385$		0			0
$386$	−8.69935	+	15.0677i	−0.442785	+	0.766927i
$387$	−0.405294	+	0.701990i	−0.0206023	+	0.0356842i
$388$	−23.4280			−1.18938
$389$	0.251504	−	0.435617i	0.0127517	−	0.0220867i	−0.859579	−	0.511003i	$-0.829274\pi$
$389$	0.251504	−	0.435617i	0.0127517	−	0.0220867i	0.872331	+	0.488916i	$0.162608\pi$
$390$	2.76625	+	7.45647i	0.140075	+	0.377573i
$391$	−24.6847			−1.24836
$392$		0			0
$393$	23.3919	+	40.5159i	1.17996	+	2.04376i
$394$	4.76895			0.240256
$395$	−6.00206	+	10.3959i	−0.301996	+	0.523073i
$396$	−5.03757	−	8.72533i	−0.253148	−	0.438464i
$397$	−2.35044			−0.117965			−0.0589827	−	0.998259i	$-0.518786\pi$
$397$	−2.35044			−0.117965			−0.0589827	+	0.998259i	$0.518786\pi$
$398$	3.46110			0.173489
$399$		0			0
$400$	2.04784	+	3.54696i	0.102392	+	0.177348i
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	−0.00396357	−	0.999992i	$-0.501262\pi$
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	0.868000	−	0.496564i	$-0.165405\pi$
$402$	6.47821	−	11.2206i	0.323104	−	0.559632i
$403$	−7.84061	−	1.33259i	−0.390569	−	0.0663810i
$404$	0.512135	+	0.887044i	0.0254797	+	0.0441321i
$405$	−6.16835	−	10.6839i	−0.306508	−	0.530887i
$406$		0			0
$407$	−6.16197	+	10.6729i	−0.305438	+	0.529034i
$408$	−11.6678	−	20.2092i	−0.577640	−	1.00050i
$409$	4.01205	+	6.94908i	0.198383	+	0.343610i	0.948004	−	0.318257i	$-0.103098\pi$
$409$	4.01205	+	6.94908i	0.198383	+	0.343610i	−0.749621	+	0.661867i	$0.769764\pi$
$410$	3.56588	+	6.17629i	0.176106	+	0.305025i
$411$	−12.3238	−	21.3454i	−0.607886	−	1.05289i
$412$	13.4033	−	23.2152i	0.660333	−	1.14373i
$413$		0			0
$414$	−6.28382	−	10.8839i	−0.308833	−	0.534914i
$415$	−0.879993	−	1.52419i	−0.0431971	−	0.0748196i
$416$	−13.4290	+	16.2065i	−0.658412	+	0.794588i
$417$	−9.80878	+	16.9893i	−0.480338	+	0.831970i
$418$	5.03738	−	8.72500i	0.246386	−	0.426754i
$419$	5.83472	+	10.1060i	0.285045	+	0.493712i	0.972620	−	0.232401i	$-0.0746582\pi$
$419$	5.83472	+	10.1060i	0.285045	+	0.493712i	−0.687575	+	0.726113i	$0.741325\pi$
$420$		0			0
$421$	−18.3381			−0.893746			−0.446873	−	0.894597i	$-0.647462\pi$
$421$	−18.3381			−0.893746			−0.446873	+	0.894597i	$0.647462\pi$
$422$	−2.61916			−0.127499
$423$	−1.78649	−	3.09429i	−0.0868621	−	0.150449i
$424$	16.9110	−	29.2907i	0.821271	−	1.42248i
$425$	−13.0242			−0.631764
$426$	6.18040	+	10.7048i	0.299441	+	0.518647i
$427$		0			0
$428$	−12.7049			−0.614117
$429$	−7.27110	−	19.5993i	−0.351052	−	0.946265i
$430$	−0.132698	+	0.229840i	−0.00639928	+	0.0110839i
$431$	−31.2435			−1.50495			−0.752474	−	0.658622i	$-0.771140\pi$
$431$	−31.2435			−1.50495			−0.752474	+	0.658622i	$0.771140\pi$
$432$	0.298671	−	0.517314i	0.0143698	−	0.0248893i
$433$	15.2756	−	26.4582i	0.734100	−	1.27150i	−0.221017	−	0.975270i	$-0.570938\pi$
$433$	15.2756	−	26.4582i	0.734100	−	1.27150i	0.955117	−	0.296229i	$-0.0957291\pi$
$434$		0			0
$435$	8.71655	−	15.0975i	0.417927	−	0.723870i
$436$	−18.0847			−0.866099
$437$	−18.6262	+	32.2615i	−0.891012	+	1.54328i
$438$	−12.8379	−	22.2358i	−0.613417	−	1.06247i
$439$	6.07361	−	10.5198i	0.289878	−	0.502083i	−0.683903	−	0.729573i	$-0.739719\pi$
$439$	6.07361	−	10.5198i	0.289878	−	0.502083i	0.973780	+	0.227490i	$0.0730520\pi$
$440$	−3.85514	−	6.67730i	−0.183787	−	0.318328i
$441$		0			0
$442$	−3.47699	−	9.37227i	−0.165384	−	0.445794i
$443$	4.23266	+	7.33118i	0.201100	+	0.348315i	0.948883	−	0.315628i	$-0.102215\pi$
$443$	4.23266	+	7.33118i	0.201100	+	0.348315i	−0.747783	+	0.663943i	$0.768882\pi$
$444$	18.4304			0.874667
$445$	1.16035			0.0550060
$446$	−6.26065			−0.296451
$447$	−23.5705			−1.11485
$448$		0			0
$449$	11.6632	−	20.2013i	0.550420	−	0.953356i	−0.447824	−	0.894122i	$-0.647801\pi$
$449$	11.6632	−	20.2013i	0.550420	−	0.953356i	0.998244	−	0.0592342i	$-0.0188659\pi$
$450$	−3.31547	−	5.74256i	−0.156293	−	0.270707i
$451$	−9.37293	−	16.2344i	−0.441354	−	0.764448i
$452$	21.3148			1.00256
$453$	−17.7469	+	30.7386i	−0.833823	+	1.44422i
$454$	9.55416			0.448399
$455$		0			0
$456$	−35.2162			−1.64915
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	−0.988325	−	0.152358i	$-0.951313\pi$
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	0.626108	+	0.779736i	$0.284647\pi$
$458$	−4.84115			−0.226212
$459$	0.949769	+	1.64505i	0.0443314	+	0.0767842i
$460$	6.09868	+	10.5632i	0.284352	+	0.492513i
$461$	4.64102	−	8.03848i	0.216154	−	0.374389i	−0.737475	−	0.675374i	$-0.763982\pi$
$461$	4.64102	−	8.03848i	0.216154	−	0.374389i	0.953629	+	0.300985i	$0.0973154\pi$
$462$		0			0
$463$	28.8283			1.33976			0.669882	−	0.742467i	$-0.266345\pi$
$463$	28.8283			1.33976			0.669882	+	0.742467i	$0.266345\pi$
$464$	6.89068			0.319892
$465$	−6.85000			−0.317661
$466$	17.8049			0.824797
$467$	1.43696	+	2.48890i	0.0664948	+	0.115172i	0.897356	−	0.441307i	$-0.145485\pi$
$467$	1.43696	+	2.48890i	0.0664948	+	0.115172i	−0.830861	+	0.556480i	$0.812152\pi$
$468$	−9.62577	+	11.6166i	−0.444951	+	0.536979i
$469$		0			0
$470$	−0.584919	−	1.01311i	−0.0269803	−	0.0467312i
$471$	−24.7825	+	42.9245i	−1.14192	+	1.97786i
$472$	5.00354	+	8.66638i	0.230307	+	0.398903i
$473$	0.348798	−	0.604136i	0.0160377	−	0.0277782i
$474$	15.9186			0.731167
$475$	−9.82754	+	17.0218i	−0.450919	+	0.781014i
$476$		0			0
$477$	19.0572	−	33.0080i	0.872569	−	1.51133i
$478$	−0.989147	+	1.71325i	−0.0452425	+	0.0783624i
$479$	−22.6082			−1.03299			−0.516497	−	0.856289i	$-0.672764\pi$
$479$	−22.6082			−1.03299			−0.516497	+	0.856289i	$0.672764\pi$
$480$	−9.06407	+	15.6994i	−0.413716	+	0.716577i
$481$	18.1929	+	3.09207i	0.829526	+	0.140986i
$482$	−4.95659			−0.225766
$483$		0			0
$484$	−3.88985	−	6.73742i	−0.176812	−	0.306247i
$485$	−20.2043			−0.917432
$486$	−7.66136	+	13.2699i	−0.347526	+	0.601933i
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	0.831704	−	0.555219i	$-0.187365\pi$
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	−0.896686	+	0.442668i	$0.854032\pi$
$488$	−11.4233			−0.517108
$489$	−9.58544			−0.433469
$490$		0			0
$491$	11.3600	+	19.6762i	0.512672	+	0.887973i	0.999892	+	0.0146943i	$0.00467751\pi$
$491$	11.3600	+	19.6762i	0.512672	+	0.887973i	−0.487220	+	0.873279i	$0.661989\pi$
$492$	−14.0172	+	24.2784i	−0.631942	+	1.09456i
$493$	−10.9561	+	18.9765i	−0.493439	+	0.854661i
$494$	−14.8726	−	2.52775i	−0.669151	−	0.113729i
$495$	−4.34440	−	7.52473i	−0.195266	−	0.338211i
$496$	−1.35378	−	2.34482i	−0.0607865	−	0.105285i
$497$		0			0
$498$	−1.16696	+	2.02123i	−0.0522926	+	0.0905734i
$499$	9.00755	+	15.6015i	0.403233	+	0.698420i	0.994114	−	0.108338i	$-0.0345530\pi$
$499$	9.00755	+	15.6015i	0.403233	+	0.698420i	−0.590881	+	0.806759i	$0.701220\pi$
$500$	8.03968	+	13.9251i	0.359545	+	0.622751i
$501$	−10.4483	−	18.0971i	−0.466798	−	0.808518i
$502$	−0.278088	−	0.481662i	−0.0124117	−	0.0214976i
$503$	15.5748	−	26.9764i	0.694447	−	1.20282i	−0.275920	−	0.961181i	$-0.588983\pi$
$503$	15.5748	−	26.9764i	0.694447	−	1.20282i	0.970367	−	0.241636i	$-0.0776841\pi$
$504$		0			0
$505$	0.441665	+	0.764987i	0.0196539	+	0.0340415i
$506$	5.40788	+	9.36673i	0.240410	+	0.416402i
$507$	−23.7285	+	20.4158i	−1.05382	+	0.906696i
$508$	−6.59858	+	11.4291i	−0.292764	+	0.507083i
$509$	19.7509	−	34.2096i	0.875444	−	1.51631i	0.0191556	−	0.999817i	$-0.493902\pi$
$509$	19.7509	−	34.2096i	0.875444	−	1.51631i	0.856289	−	0.516497i	$-0.172764\pi$
$510$	−4.30499	−	7.45647i	−0.190628	−	0.330178i
$511$		0			0
$512$	−13.2606			−0.586042
$513$	2.86664			0.126565
$514$	1.15707	+	2.00411i	0.0510363	+	0.0883974i
$515$	11.5590	−	20.0208i	0.509351	−	0.882221i
$516$	−1.04325			−0.0459265
$517$	1.53746	+	2.66296i	0.0676174	+	0.117117i
$518$		0			0
$519$	2.24880			0.0987115
$520$	−7.36639	+	8.88995i	−0.323038	+	0.389850i
$521$	8.88359	−	15.3868i	0.389197	−	0.674109i	−0.603145	−	0.797632i	$-0.706086\pi$
$521$	8.88359	−	15.3868i	0.389197	−	0.674109i	0.992342	+	0.123523i	$0.0394192\pi$
$522$	−11.1561			−0.488288
$523$	0.894522	−	1.54936i	0.0391147	−	0.0677487i	−0.845805	−	0.533492i	$-0.820880\pi$
$523$	0.894522	−	1.54936i	0.0391147	−	0.0677487i	0.884920	+	0.465743i	$0.154213\pi$
$524$	−14.5283	+	25.1637i	−0.634671	+	1.09928i
$525$		0			0
$526$	10.5062	−	18.1972i	0.458091	−	0.793438i
$527$	8.60999			0.375057
$528$	3.55842	−	6.16336i	0.154860	−	0.268226i
$529$	−8.49616	−	14.7158i	−0.369398	−	0.639817i
$530$	6.23956	−	10.8072i	0.271029	−	0.469436i
$531$	5.63854	+	9.76624i	0.244692	+	0.423819i
$532$		0			0
$533$	−17.9098	+	21.6140i	−0.775758	+	0.936205i
$534$	−0.769371	−	1.33259i	−0.0332939	−	0.0576668i
$535$	−10.9568			−0.473702
$536$	18.8087			0.812412
$537$	32.6174			1.40754
$538$	−0.878269			−0.0378649
$539$		0			0
$540$	0.469305	−	0.812860i	0.0201957	−	0.0349799i
$541$	−7.70135	−	13.3391i	−0.331107	−	0.573494i	0.651622	−	0.758544i	$-0.274089\pi$
$541$	−7.70135	−	13.3391i	−0.331107	−	0.573494i	−0.982729	+	0.185050i	$0.940755\pi$
$542$	8.95214	+	15.5056i	0.384527	+	0.666021i
$543$	−21.3403			−0.915801
$544$	11.3929	−	19.7331i	0.488467	−	0.846050i
$545$	−15.5962			−0.668069
$546$		0			0
$547$	−3.96944			−0.169721			−0.0848605	−	0.996393i	$-0.527044\pi$
$547$	−3.96944			−0.169721			−0.0848605	+	0.996393i	$0.527044\pi$
$548$	7.65406	−	13.2572i	0.326965	−	0.566321i
$549$	−12.8730			−0.549408
$550$	2.85330	+	4.94207i	0.121665	+	0.210731i
$551$	16.5342	+	28.6380i	0.704379	+	1.22002i
$552$	18.9032	−	32.7413i	0.804574	−	1.39356i
$553$		0			0
$554$	−6.77331			−0.287770
$555$	15.8944			0.674678
$556$	−12.1841			−0.516722
$557$	18.6901			0.791924			0.395962	−	0.918267i	$-0.370411\pi$
$557$	18.6901			0.791924			0.395962	+	0.918267i	$0.370411\pi$
$558$	2.19178	+	3.79628i	0.0927856	+	0.160709i
$559$	−1.02981	−	0.175026i	−0.0435563	−	0.00740282i
$560$		0			0
$561$	11.3157	+	19.5993i	0.477749	+	0.827485i
$562$	3.39711	−	5.88397i	0.143298	−	0.248200i
$563$	−18.1530	−	31.4418i	−0.765056	−	1.32512i	−0.940217	−	0.340576i	$-0.889378\pi$
$563$	−18.1530	−	31.4418i	−0.765056	−	1.32512i	0.175161	−	0.984540i	$-0.443955\pi$
$564$	2.29926	−	3.98244i	0.0968163	−	0.167691i
$565$	18.3819			0.773333
$566$	4.06001	−	7.03215i	0.170655	−	0.295583i
$567$		0			0
$568$	−8.97201	+	15.5400i	−0.376457	+	0.652043i
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	−0.957828	−	0.287343i	$-0.907228\pi$
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	0.727760	+	0.685832i	$0.240562\pi$
$570$	−12.9936			−0.544240
$571$	−15.6682	+	27.1380i	−0.655692	+	1.13569i	0.326028	+	0.945360i	$0.394290\pi$
$571$	−15.6682	+	27.1380i	−0.655692	+	1.13569i	−0.981720	+	0.190332i	$0.939044\pi$
$572$	8.28398	−	9.99733i	0.346371	−	0.418009i
$573$	−37.0175			−1.54643
$574$		0			0
$575$	−10.5504	−	18.2738i	−0.439981	−	0.762069i
$576$	4.73210			0.197171
$577$	21.3938	−	37.0552i	0.890636	−	1.54263i	0.0515210	−	0.998672i	$-0.483593\pi$
$577$	21.3938	−	37.0552i	0.890636	−	1.54263i	0.839115	−	0.543954i	$-0.183074\pi$
$578$	−0.626353	−	1.08487i	−0.0260528	−	0.0451248i
$579$	−58.9819			−2.45120
$580$	10.8274			0.449583
$581$		0			0
$582$	13.3965	+	23.2034i	0.555302	+	0.961811i
$583$	−16.4007	+	28.4069i	−0.679248	+	1.17649i
$584$	18.6366	−	32.2795i	0.771187	−	1.33573i
$585$	−8.30127	+	10.0182i	−0.343215	+	0.414201i
$586$	−3.32259	−	5.75489i	−0.137255	−	0.237732i
$587$	19.3943	+	33.5919i	0.800488	+	1.38649i	0.919296	+	0.393568i	$0.128759\pi$
$587$	19.3943	+	33.5919i	0.800488	+	1.38649i	−0.118808	+	0.992917i	$0.537907\pi$
$588$		0			0
$589$	6.49678	−	11.2527i	0.267695	−	0.463661i
$590$	1.84613	+	3.19759i	0.0760039	+	0.131643i
$591$	8.08341	+	14.0009i	0.332507	+	0.575919i
$592$	3.14124	+	5.44078i	0.129104	+	0.223615i
$593$	14.9782	+	25.9430i	0.615081	+	1.06535i	0.990370	+	0.138443i	$0.0442099\pi$
$593$	14.9782	+	25.9430i	0.615081	+	1.06535i	−0.375290	+	0.926908i	$0.622457\pi$
$594$	0.416147	−	0.720787i	0.0170747	−	0.0295743i
$595$		0			0
$596$	−7.31960	−	12.6779i	−0.299823	−	0.519308i
$597$	5.86658	+	10.1612i	0.240103	+	0.415871i
$598$	10.3334	−	12.4706i	0.422562	−	0.509959i
$599$	−20.6269	+	35.7269i	−0.842794	+	1.45976i	0.0447293	+	0.998999i	$0.485757\pi$
$599$	−20.6269	+	35.7269i	−0.842794	+	1.45976i	−0.887523	+	0.460763i	$0.847576\pi$
$600$	9.97371	−	17.2750i	0.407175	−	0.705248i
$601$	−3.30544	−	5.72520i	−0.134832	−	0.233536i	0.790701	−	0.612202i	$-0.209716\pi$
$601$	−3.30544	−	5.72520i	−0.134832	−	0.233536i	−0.925533	+	0.378666i	$0.876383\pi$
$602$		0			0
$603$	21.1957			0.863156
$604$	−22.0446			−0.896982
$605$	−3.35461	−	5.81036i	−0.136384	−	0.236225i
$606$	0.585692	−	1.01445i	0.0237921	−	0.0412091i
$607$	−20.8832			−0.847622			−0.423811	−	0.905751i	$-0.639308\pi$
$607$	−20.8832			−0.847622			−0.423811	+	0.905751i	$0.639308\pi$
$608$	−17.1933	−	29.7797i	−0.697282	−	1.20773i
$609$		0			0
$610$	−4.21479			−0.170652
$611$	2.93777	−	3.54538i	0.118850	−	0.143431i
$612$	8.16632	−	14.1445i	0.330104	−	0.571757i
$613$	−4.29655			−0.173536			−0.0867680	−	0.996229i	$-0.527654\pi$
$613$	−4.29655			−0.173536			−0.0867680	+	0.996229i	$0.527654\pi$
$614$	2.88181	−	4.99144i	0.116300	−	0.201438i
$615$	−12.0884	+	20.9377i	−0.487451	+	0.844290i
$616$		0			0
$617$	15.3690	−	26.6199i	0.618732	−	1.07167i	−0.370986	−	0.928639i	$-0.620980\pi$
$617$	15.3690	−	26.6199i	0.618732	−	1.07167i	0.989717	−	0.143036i	$-0.0456866\pi$
$618$	−30.6568			−1.23320
$619$	10.3208	−	17.8762i	0.414829	−	0.718505i	−0.580581	−	0.814202i	$-0.697175\pi$
$619$	10.3208	−	17.8762i	0.414829	−	0.718505i	0.995410	+	0.0956971i	$0.0305080\pi$
$620$	−2.12721	−	3.68443i	−0.0854307	−	0.147970i
$621$	−1.53874	+	2.66518i	−0.0617476	+	0.106950i
$622$	−3.06849	−	5.31479i	−0.123035	−	0.213104i
$623$		0			0
$624$	−10.5060	−	1.78561i	−0.420578	−	0.0714815i
$625$	−1.40818	−	2.43904i	−0.0563272	−	0.0975616i
$626$	3.71290			0.148397
$627$	34.1536			1.36396
$628$	−30.7839			−1.22841
$629$	−19.9781			−0.796580
$630$		0			0
$631$	−14.6683	+	25.4063i	−0.583937	+	1.01141i	0.411070	+	0.911604i	$0.365155\pi$
$631$	−14.6683	+	25.4063i	−0.583937	+	1.01141i	−0.995007	+	0.0998043i	$0.968178\pi$
$632$	11.5544	+	20.0129i	0.459611	+	0.796069i
$633$	−4.43950	−	7.68943i	−0.176454	−	0.305628i
$634$	−7.95019			−0.315742
$635$	−5.69061	+	9.85643i	−0.225825	+	0.391141i
$636$	49.0543			1.94513
$637$		0			0
$638$	9.60097			0.380106
$639$	−10.1107	+	17.5122i	−0.399971	+	0.692771i
$640$	−13.5080			−0.533950
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	0.902960	−	0.429725i	$-0.141390\pi$
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	−0.823633	+	0.567124i	$0.808056\pi$
$642$	7.26486	+	12.5831i	0.286721	+	0.496616i
$643$	3.43641	−	5.95203i	0.135519	−	0.234725i	−0.790277	−	0.612750i	$-0.790063\pi$
$643$	3.43641	−	5.95203i	0.135519	−	0.234725i	0.925795	+	0.378025i	$0.123397\pi$
$644$		0			0
$645$	−0.899698			−0.0354256
$646$	16.3320			0.642574
$647$	−33.7431			−1.32658			−0.663289	−	0.748363i	$-0.730840\pi$
$647$	−33.7431			−1.32658			−0.663289	+	0.748363i	$0.730840\pi$
$648$	−23.7491			−0.932955
$649$	−4.85256	−	8.40487i	−0.190479	−	0.329920i
$650$	5.45208	−	6.57972i	0.213848	−	0.258078i
$651$		0			0
$652$	−2.97667	−	5.15575i	−0.116576	−	0.201915i
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	0.352777	+	0.935708i	$0.385238\pi$
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	−0.986735	+	0.162340i	$0.948096\pi$
$654$	10.3411	+	17.9113i	0.404368	+	0.700385i
$655$	−12.5292	+	21.7012i	−0.489556	+	0.847936i
$656$	−9.55622			−0.373108
$657$	21.0018	−	36.3761i	0.819357	−	1.41917i
$658$		0			0
$659$	−2.00518	+	3.47307i	−0.0781106	+	0.135291i	−0.902435	−	0.430827i	$-0.858222\pi$
$659$	−2.00518	+	3.47307i	−0.0781106	+	0.135291i	0.824324	+	0.566118i	$0.191555\pi$
$660$	5.59137	−	9.68453i	0.217644	−	0.376970i
$661$	−1.81794			−0.0707097			−0.0353549	−	0.999375i	$-0.511256\pi$
$661$	−1.81794			−0.0707097			−0.0353549	+	0.999375i	$0.511256\pi$
$662$	7.11947	−	12.3313i	0.276706	−	0.479269i
$663$	21.6220	−	26.0940i	0.839727	−	1.01341i
$664$	−3.38811			−0.131484
$665$		0			0
$666$	−5.08569	−	8.80868i	−0.197067	−	0.341329i
$667$	−35.5005			−1.37459
$668$	6.48928	−	11.2398i	0.251078	−	0.434880i
$669$	−10.6119	−	18.3803i	−0.410278	−	0.710622i
$670$	6.93974			0.268106
$671$	11.0786			0.427684
$672$		0			0
$673$	11.4871	+	19.8963i	0.442797	+	0.766947i	0.997896	−	0.0648375i	$-0.0206529\pi$
$673$	11.4871	+	19.8963i	0.442797	+	0.766947i	−0.555099	+	0.831784i	$0.687320\pi$
$674$	6.60091	−	11.4331i	0.254258	−	0.440387i
$675$	−0.811871	+	1.40620i	−0.0312489	+	0.0541247i
$676$	−18.3498	−	6.42298i	−0.705760	−	0.247038i
$677$	−19.0138	−	32.9329i	−0.730760	−	1.26571i	−0.956559	−	0.291540i	$-0.905832\pi$
$677$	−19.0138	−	32.9329i	−0.730760	−	1.26571i	0.225799	−	0.974174i	$-0.427501\pi$
$678$	−12.1881	−	21.1104i	−0.468081	−	0.810741i
$679$		0			0
$680$	6.24950	−	10.8245i	0.239658	−	0.415099i
$681$	16.1944	+	28.0495i	0.620570	+	1.07486i
$682$	−1.88626	−	3.26709i	−0.0722285	−	0.125103i
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	0.931839	+	0.362872i	$0.118204\pi$
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	−0.151663	+	0.988432i	$0.548463\pi$
$684$	−12.3240	−	21.3458i	−0.471220	−	0.816177i
$685$	6.60087	−	11.4330i	0.252206	−	0.436834i
$686$		0			0
$687$	−8.20578	−	14.2128i	−0.313070	−	0.542253i
$688$	−0.177809	−	0.307975i	−0.00677892	−	0.0117414i
$689$	48.4223	+	8.22985i	1.84474	+	0.313532i
$690$	6.97462	−	12.0804i	0.265519	−	0.459893i
$691$	1.56434	−	2.70952i	0.0595104	−	0.103075i	−0.834735	−	0.550651i	$-0.814379\pi$
$691$	1.56434	−	2.70952i	0.0595104	−	0.103075i	0.894246	+	0.447576i	$0.147713\pi$
$692$	0.698346	+	1.20957i	0.0265471	+	0.0459809i
$693$		0			0
$694$	−15.8690			−0.602378
$695$	−10.5076			−0.398576
$696$	−16.7801	−	29.0639i	−0.636047	−	1.10167i
$697$	15.1943	−	26.3173i	0.575525	−	0.996838i
$698$	−6.24080			−0.236218
$699$	30.1795	+	52.2724i	1.14149	+	1.97712i
$700$		0			0
$701$	9.61382			0.363109			0.181555	−	0.983381i	$-0.441887\pi$
$701$	9.61382			0.363109			0.181555	+	0.983381i	$0.441887\pi$
$702$	−1.22865	−	0.208822i	−0.0463725	−	0.00788147i
$703$	−15.0748	+	26.1102i	−0.568555	+	0.984767i
$704$	−4.07247			−0.153487
$705$	1.98288	−	3.43445i	0.0746797	−	0.129349i
$706$	2.74134	−	4.74815i	0.103172	−	0.178699i
$707$		0			0
$708$	−7.25696	+	12.5694i	−0.272733	+	0.472388i
$709$	28.1294			1.05642			0.528211	−	0.849113i	$-0.322863\pi$
$709$	28.1294			1.05642			0.528211	+	0.849113i	$0.322863\pi$
$710$	−3.31035	+	5.73370i	−0.124235	+	0.215182i
$711$	13.0208	+	22.5527i	0.488319	+	0.845794i
$712$	1.11689	−	1.93450i	0.0418571	−	0.0724986i
$713$	6.97462	+	12.0804i	0.261201	+	0.452414i
$714$		0			0
$715$	7.14411	−	8.62170i	0.267174	−	0.322433i
$716$	10.1290	+	17.5440i	0.378540	+	0.655651i
$717$	−6.70645			−0.250457
$718$	7.52594			0.280865
$719$	24.9044			0.928779			0.464389	−	0.885631i	$-0.346274\pi$
$719$	24.9044			0.928779			0.464389	+	0.885631i	$0.346274\pi$
$720$	−4.42936			−0.165073
$721$		0			0
$722$	5.57581	−	9.65758i	0.207510	−	0.359418i
$723$	−8.40146	−	14.5517i	−0.312454	−	0.541185i
$724$	−6.62705	−	11.4784i	−0.246292	−	0.426591i
$725$	−18.7308			−0.695643
$726$	−4.44854	+	7.70510i	−0.165101	+	0.285963i
$727$	−24.2120			−0.897974			−0.448987	−	0.893538i	$-0.648215\pi$
$727$	−24.2120			−0.897974			−0.448987	+	0.893538i	$0.648215\pi$
$728$		0			0
$729$	−23.2479			−0.861032
$730$	6.87624	−	11.9100i	0.254501	−	0.440808i
$731$	1.13086			0.0418264
$732$	−8.28398	−	14.3483i	−0.306185	−	0.530328i
$733$	6.19943	+	10.7377i	0.228981	+	0.396607i	0.957506	−	0.288412i	$-0.0931272\pi$
$733$	6.19943	+	10.7377i	0.228981	+	0.396607i	−0.728525	+	0.685019i	$0.759794\pi$
$734$	2.06717	−	3.58045i	0.0763007	−	0.132157i
$735$		0			0
$736$	36.9159			1.36074
$737$	−18.2411			−0.671921
$738$	15.4716			0.569518
$739$	−10.9604			−0.403184			−0.201592	−	0.979470i	$-0.564612\pi$
$739$	−10.9604			−0.403184			−0.201592	+	0.979470i	$0.564612\pi$
$740$	4.93585	+	8.54915i	0.181446	+	0.314273i
$741$	−17.7881	−	47.9482i	−0.653463	−	1.76142i
$742$		0			0
$743$	−20.3462	−	35.2407i	−0.746431	−	1.29286i	−0.949523	−	0.313697i	$-0.898432\pi$
$743$	−20.3462	−	35.2407i	−0.746431	−	1.29286i	0.203092	−	0.979160i	$-0.434901\pi$
$744$	−6.59340	+	11.4201i	−0.241726	+	0.418681i
$745$	−6.31243	−	10.9334i	−0.231269	−	0.400570i
$746$	9.25393	−	16.0283i	0.338810	−	0.586837i
$747$	−3.81810			−0.139697
$748$	−7.02797	+	12.1728i	−0.256968	+	0.445082i
$749$		0			0
$750$	9.19439	−	15.9252i	0.335732	−	0.581505i
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	−0.938976	−	0.343981i	$-0.888224\pi$
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	0.767385	+	0.641187i	$0.221558\pi$
$752$	1.56753			0.0571618
$753$	0.942721	−	1.63284i	0.0343547	−	0.0595040i
$754$	−5.00045	−	13.4788i	−0.182106	−	0.490868i
$755$	−19.0113			−0.691890
$756$		0			0
$757$	14.7904	+	25.6177i	0.537566	+	0.931091i	0.999034	+	0.0439345i	$0.0139893\pi$
$757$	14.7904	+	25.6177i	0.537566	+	0.931091i	−0.461469	+	0.887156i	$0.652677\pi$
$758$	−11.1183			−0.403834
$759$	−18.3328	+	31.7533i	−0.665439	+	1.15257i
$760$	−9.43129	−	16.3355i	−0.342109	−	0.592550i
$761$	16.9417			0.614137			0.307068	−	0.951687i	$-0.400652\pi$
$761$	16.9417			0.614137			0.307068	+	0.951687i	$0.400652\pi$
$762$	15.0926			0.546748
$763$		0			0
$764$	−11.4955	−	19.9107i	−0.415891	−	0.720345i
$765$	7.04264	−	12.1982i	0.254627	−	0.441027i
$766$	−4.46017	+	7.72524i	−0.161152	+	0.279124i
$767$	−9.27224	+	11.1900i	−0.334801	+	0.404047i
$768$	13.0289	+	22.5668i	0.470141	+	0.814308i
$769$	−3.68287	−	6.37892i	−0.132808	−	0.230030i	0.791950	−	0.610586i	$-0.209066\pi$
$769$	−3.68287	−	6.37892i	−0.132808	−	0.230030i	−0.924758	+	0.380556i	$0.875733\pi$
$770$		0			0
$771$	−3.92249	+	6.79396i	−0.141265	+	0.244678i
$772$	−18.3163	−	31.7248i	−0.659218	−	1.14180i
$773$	22.3867	+	38.7749i	0.805194	+	1.39464i	0.916160	+	0.400813i	$0.131272\pi$
$773$	22.3867	+	38.7749i	0.805194	+	1.39464i	−0.110966	+	0.993824i	$0.535394\pi$
$774$	0.287875	+	0.498614i	0.0103475	+	0.0179223i
$775$	3.67995	+	6.37385i	0.132188	+	0.228956i
$776$	−19.4475	+	33.6840i	−0.698124	+	1.20919i
$777$		0			0
$778$	−0.178640	−	0.309413i	−0.00640454	−	0.0110930i
$779$	−22.9301	−	39.7161i	−0.821556	−	1.42298i
$780$	−16.5082	−	2.80574i	−0.591090	−	0.100462i
$781$	8.70127	−	15.0710i	0.311356	−	0.539284i
$782$	−8.76662	+	15.1842i	−0.313494	+	0.542987i
$783$	1.36592	+	2.36583i	0.0488138	+	0.0845480i
$784$		0			0
$785$	−26.5480			−0.947540
$786$	33.2299			1.18527
$787$	9.38412	+	16.2538i	0.334508	+	0.579385i	0.983390	−	0.181504i	$-0.0580966\pi$
$787$	9.38412	+	16.2538i	0.334508	+	0.579385i	−0.648882	+	0.760889i	$0.724763\pi$
$788$	−5.02046	+	8.69570i	−0.178847	+	0.309771i
$789$	71.2322			2.53594
$790$	4.26318	+	7.38404i	0.151677	+	0.262713i
$791$		0			0
$792$	−16.7267			−0.594356
$793$	−5.77004	−	15.5532i	−0.204900	−	0.552311i
$794$	−0.834744	+	1.44582i	−0.0296240	+	0.0513102i
$795$	42.3044			1.50038
$796$	−3.64363	+	6.31095i	−0.129145	+	0.223686i
$797$	−3.60849	+	6.25008i	−0.127819	+	0.221389i	−0.922831	−	0.385204i	$-0.874131\pi$
$797$	−3.60849	+	6.25008i	−0.127819	+	0.221389i	0.795012	+	0.606593i	$0.207464\pi$
$798$		0			0
$799$	−2.49235	+	4.31687i	−0.0881730	+	0.152720i
$800$	19.4775			0.688635
$801$	1.25863	−	2.18001i	0.0444716	−	0.0770270i
$802$	−12.2896	−	21.2862i	−0.433961	−	0.751643i
$803$	−18.0742	+	31.3054i	−0.637825	+	1.10474i
$804$	13.6397	+	23.6247i	0.481036	+	0.833180i
$805$		0			0
$806$	−3.60425	+	4.34971i	−0.126954	+	0.153212i
$807$	−1.48867	−	2.57846i	−0.0524037	−	0.0907659i
$808$	1.70048			0.0598228
$809$	14.8318			0.521459			0.260729	−	0.965412i	$-0.416037\pi$
$809$	14.8318			0.521459			0.260729	+	0.965412i	$0.416037\pi$
$810$	−8.76260			−0.307886
$811$	18.5831			0.652541			0.326271	−	0.945276i	$-0.394208\pi$
$811$	18.5831			0.652541			0.326271	+	0.945276i	$0.394208\pi$
$812$		0			0
$813$	−30.3479	+	52.5641i	−1.06435	+	1.84350i
$814$	4.37677	+	7.58078i	0.153406	+	0.265706i
$815$	−2.56708	−	4.44632i	−0.0899210	−	0.155748i
$816$	11.5370			0.403875
$817$	0.853305	−	1.47797i	0.0298534	−	0.0517075i
$818$	5.69942			0.199275
$819$		0			0
$820$	−15.0158			−0.524374
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	−0.534598	−	0.845106i	$-0.679537\pi$
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	0.999183	+	0.0404222i	$0.0128703\pi$
$822$	−17.5068			−0.610620
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	0.801175	−	0.598431i	$-0.204209\pi$
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	−0.918843	+	0.394622i	$0.870875\pi$
$824$	−22.2520	−	38.5416i	−0.775186	−	1.34266i
$825$	−9.67275	+	16.7537i	−0.336762	+	0.583289i
$826$		0			0
$827$	−21.7430			−0.756079			−0.378039	−	0.925789i	$-0.623402\pi$
$827$	−21.7430			−0.756079			−0.378039	+	0.925789i	$0.623402\pi$
$828$	26.4609			0.919579
$829$	−14.6216			−0.507828			−0.253914	−	0.967227i	$-0.581718\pi$
$829$	−14.6216			−0.507828			−0.253914	+	0.967227i	$0.581718\pi$
$830$	−1.25009			−0.0433914
$831$	−11.4808	−	19.8853i	−0.398265	−	0.689815i
$832$	2.12105	+	5.71733i	0.0735343	+	0.198213i
$833$		0			0
$834$	6.96705	+	12.0673i	0.241249	+	0.417856i
$835$	5.59636	−	9.69318i	0.193670	−	0.335446i
$836$	10.6061	+	18.3703i	0.366819	+	0.635350i
$837$	0.536710	−	0.929609i	0.0185514	−	0.0321320i
$838$	8.28865			0.286327
$839$	5.37343	−	9.30705i	0.185511	−	0.321315i	−0.758237	−	0.651979i	$-0.773939\pi$
$839$	5.37343	−	9.30705i	0.185511	−	0.321315i	0.943749	+	0.330663i	$0.107273\pi$
$840$		0			0
$841$	−1.25660	+	2.17649i	−0.0433310	+	0.0750515i
$842$	−6.51267	+	11.2803i	−0.224441	+	0.388744i
$843$	23.0325			0.793282
$844$	2.75729	−	4.77577i	0.0949099	−	0.164389i
$845$	−15.8248	−	5.53918i	−0.544391	−	0.190554i
$846$	−2.53784			−0.0872527
$847$		0			0
$848$	8.36071	+	14.4812i	0.287108	+	0.497286i
$849$	27.5270			0.944724
$850$	−4.62544	+	8.01150i	−0.158651	+	0.274792i
$851$	−16.1835	−	28.0307i	−0.554764	−	0.960879i
$852$	−26.0254			−0.891615
$853$	−31.7709			−1.08782			−0.543908	−	0.839145i	$-0.683056\pi$
$853$	−31.7709			−1.08782			−0.543908	+	0.839145i	$0.683056\pi$
$854$		0			0
$855$	−10.6282	−	18.4086i	−0.363478	−	0.629562i
$856$	−10.5463	+	18.2667i	−0.360466	+	0.624345i
$857$	0.324052	−	0.561275i	0.0110694	−	0.0191728i	−0.860438	−	0.509556i	$-0.829810\pi$
$857$	0.324052	−	0.561275i	0.0110694	−	0.0191728i	0.871507	+	0.490383i	$0.163143\pi$
$858$	−14.6384	−	2.48793i	−0.499745	−	0.0849366i
$859$	21.5951	+	37.4038i	0.736815	+	1.27620i	0.953923	+	0.300053i	$0.0970043\pi$
$859$	21.5951	+	37.4038i	0.736815	+	1.27620i	−0.217108	+	0.976148i	$0.569662\pi$
$860$	−0.279393	−	0.483923i	−0.00952723	−	0.0165017i
$861$		0			0
$862$	−11.0959	+	19.2187i	−0.377929	+	0.654592i
$863$	−10.8047	−	18.7143i	−0.367796	−	0.637042i	0.621425	−	0.783474i	$-0.286554\pi$
$863$	−10.8047	−	18.7143i	−0.367796	−	0.637042i	−0.989221	+	0.146432i	$0.953221\pi$
$864$	−1.42037	−	2.46016i	−0.0483220	−	0.0836962i
$865$	0.602253	+	1.04313i	0.0204772	+	0.0354676i
$866$	−10.8501	−	18.7929i	−0.368701	−	0.638608i
$867$	2.12335	−	3.67774i	0.0721126	−	0.124903i
$868$		0			0
$869$	−11.2058	−	19.4090i	−0.380130	−	0.658405i
$870$	−6.19125	−	10.7236i	−0.209903	−	0.363563i
$871$	9.50048	+	25.6087i	0.321912	+	0.867717i
$872$	−15.0120	+	26.0015i	−0.508370	+	0.880523i
$873$	−21.9156	+	37.9589i	−0.741731	+	1.28472i
$874$	13.2299	+	22.9149i	0.447509	+	0.775109i
$875$		0			0
$876$	54.0597			1.82651
$877$	−0.880766			−0.0297413			−0.0148707	−	0.999889i	$-0.504734\pi$
$877$	−0.880766			−0.0297413			−0.0148707	+	0.999889i	$0.504734\pi$
$878$	−4.31401	−	7.47208i	−0.145591	−	0.252170i
$879$	11.2636	−	19.5092i	0.379912	−	0.658027i
$880$	3.81193			0.128500
$881$	0.0700176	+	0.121274i	0.00235895	+	0.00408583i	0.867202	−	0.497956i	$-0.165916\pi$
$881$	0.0700176	+	0.121274i	0.00235895	+	0.00408583i	−0.864844	+	0.502042i	$0.832582\pi$
$882$		0			0
$883$	−18.8253			−0.633522			−0.316761	−	0.948505i	$-0.602595\pi$
$883$	−18.8253			−0.633522			−0.316761	+	0.948505i	$0.602595\pi$
$884$	20.7497	+	3.52662i	0.697889	+	0.118613i
$885$	−6.25841	+	10.8399i	−0.210374	+	0.364378i
$886$	6.01281			0.202004
$887$	16.6505	−	28.8395i	0.559069	−	0.968337i	−0.438505	−	0.898729i	$-0.644492\pi$
$887$	16.6505	−	28.8395i	0.559069	−	0.968337i	0.997574	−	0.0696078i	$-0.0221748\pi$
$888$	15.2990	−	26.4986i	0.513400	−	0.889234i
$889$		0			0
$890$	0.412092	−	0.713764i	0.0138133	−	0.0239254i
$891$	23.0325			0.771618
$892$	6.59084	−	11.4157i	0.220677	−	0.382225i
$893$	3.76127	+	6.51471i	0.125866	+	0.218006i
$894$	−8.37090	+	14.4988i	−0.279965	+	0.484913i
$895$	8.73529	+	15.1300i	0.291989	+	0.505739i
$896$		0			0
$897$	54.1267	+	9.19937i	1.80724	+	0.307158i
$898$	−8.28421	−	14.3487i	−0.276448	−	0.478822i
$899$	12.3825			0.412980
$900$	13.9613			0.465376
$901$	−53.1738			−1.77148
$902$	−13.3149			−0.443339
$903$		0			0
$904$	17.6933	−	30.6457i	0.588471	−	1.01926i
$905$	−5.71517	−	9.89896i	−0.189979	−	0.329052i
$906$	12.6054	+	21.8332i	0.418786	+	0.725359i
$907$	11.5870			0.384740			0.192370	−	0.981322i	$-0.438383\pi$
$907$	11.5870			0.384740			0.192370	+	0.981322i	$0.438383\pi$
$908$	−10.0580	+	17.4210i	−0.333788	+	0.578137i
$909$	1.91629			0.0635594
$910$		0			0
$911$	52.5489			1.74102			0.870512	−	0.492147i	$-0.163788\pi$
$911$	52.5489			1.74102			0.870512	+	0.492147i	$0.163788\pi$
$912$	8.70537	−	15.0781i	0.288264	−	0.499287i
$913$	3.28588			0.108747
$914$	5.49998	+	9.52624i	0.181923	+	0.315100i
$915$	−7.14411	−	12.3740i	−0.236177	−	0.409070i
$916$	5.09646	−	8.82733i	0.168392	−	0.291663i
$917$		0			0
$918$	1.34922			0.0445308
$919$	−20.0534			−0.661502			−0.330751	−	0.943718i	$-0.607302\pi$
$919$	−20.0534			−0.661502			−0.330751	+	0.943718i	$0.607302\pi$
$920$	20.2499			0.667621
$921$	19.5387			0.643823
$922$	−3.29645	−	5.70963i	−0.108563	−	0.188036i
$923$	−25.6901	−	4.36628i	−0.845599	−	0.143718i
$924$		0			0
$925$	−8.53874	−	14.7895i	−0.280752	−	0.486277i
$926$	10.2382	−	17.7330i	0.336447	−	0.582744i
$927$	−25.0760	−	43.4330i	−0.823605	−	1.42653i
$928$	16.3848	−	28.3793i	0.537857	−	0.931596i
$929$	−15.9085			−0.521941			−0.260971	−	0.965347i	$-0.584043\pi$
$929$	−15.9085			−0.521941			−0.260971	+	0.965347i	$0.584043\pi$
$930$	−2.43273	+	4.21361i	−0.0797724	+	0.138170i
$931$		0			0
$932$	−18.7439	+	32.4655i	−0.613978	+	1.06344i
$933$	10.4022	−	18.0172i	0.340554	−	0.589857i
$934$	2.04131			0.0667938
$935$	−6.06092	+	10.4978i	−0.198213	+	0.343316i
$936$	8.71171	+	23.4825i	0.284751	+	0.767550i
$937$	26.1978			0.855846			0.427923	−	0.903815i	$-0.359245\pi$
$937$	26.1978			0.855846			0.427923	+	0.903815i	$0.359245\pi$
$938$		0			0
$939$	6.29339	+	10.9005i	0.205377	+	0.355723i
$940$	2.46307			0.0803364
$941$	18.1529	−	31.4418i	0.591769	−	1.02497i	−0.402225	−	0.915541i	$-0.631763\pi$
$941$	18.1529	−	31.4418i	0.591769	−	1.02497i	0.993994	−	0.109433i	$-0.0349035\pi$
$942$	17.6026	+	30.4887i	0.573525	+	0.993375i
$943$	49.2332			1.60325
$944$	−4.94745			−0.161026
$945$		0			0
$946$	−0.247746	−	0.429109i	−0.00805493	−	0.0139516i
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	−0.858464	−	0.512873i	$-0.828581\pi$
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	0.873393	+	0.487015i	$0.161914\pi$
$948$	−16.7582	+	29.0260i	−0.544280	+	0.942720i
$949$	53.3632	+	9.06960i	1.73224	+	0.294412i
$950$	6.98037	+	12.0904i	0.226473	+	0.392263i
$951$	−13.4756	−	23.3405i	−0.436977	−	0.756867i
$952$		0			0
$953$	9.17943	−	15.8992i	0.297351	−	0.515027i	−0.678178	−	0.734898i	$-0.737230\pi$
$953$	9.17943	−	15.8992i	0.297351	−	0.515027i	0.975529	+	0.219871i	$0.0705635\pi$
$954$	−13.5361	−	23.4452i	−0.438247	−	0.759065i
$955$	−9.91370	−	17.1710i	−0.320800	−	0.555641i
$956$	−2.08263	−	3.60722i	−0.0673570	−	0.116666i
$957$	16.2737	+	28.1869i	0.526055	+	0.911153i
$958$	−8.02914	+	13.9069i	−0.259410	+	0.449311i
$959$		0			0
$960$	2.62616	+	4.54864i	0.0847589	+	0.146807i
$961$	13.0673	+	22.6332i	0.421525	+	0.730102i
$962$	8.36311	−	10.0928i	0.269637	−	0.325406i
$963$	−11.8848	+	20.5850i	−0.382981	+	0.663343i
$964$	5.21800	−	9.03783i	0.168060	−	0.291089i
$965$	−15.7960	−	27.3594i	−0.508491	−	0.880731i
$966$		0			0
$967$	12.5923			0.404940			0.202470	−	0.979288i	$-0.435103\pi$
$967$	12.5923			0.404940			0.202470	+	0.979288i	$0.435103\pi$
$968$	−12.9158			−0.415129
$969$	27.6829	+	47.9482i	0.889302	+	1.54032i
$970$	−7.17544	+	12.4282i	−0.230389	+	0.399046i
$971$	−21.3308			−0.684537			−0.342269	−	0.939602i	$-0.611195\pi$
$971$	−21.3308			−0.684537			−0.342269	+	0.939602i	$0.611195\pi$
$972$	−16.1308	−	27.9394i	−0.517397	−	0.896157i
$973$		0			0
$974$	−2.03712			−0.0652736
$975$	28.5583	+	4.85377i	0.914598	+	0.155445i
$976$	2.82381	−	4.89098i	0.0903880	−	0.156557i
$977$	−42.4279			−1.35739			−0.678695	−	0.734420i	$-0.737454\pi$
$977$	−42.4279			−1.35739			−0.678695	+	0.734420i	$0.737454\pi$
$978$	−3.40421	+	5.89626i	−0.108854	+	0.188542i
$979$	−1.08318	+	1.87613i	−0.0346187	+	0.0599614i
$980$		0			0
$981$	−16.9172	+	29.3014i	−0.540124	+	0.935523i
$982$	16.1378			0.514977
$983$	−1.04879	+	1.81655i	−0.0334511	+	0.0579391i	−0.882266	−	0.470751i	$-0.843983\pi$
$983$	−1.04879	+	1.81655i	−0.0334511	+	0.0579391i	0.848815	+	0.528690i	$0.177316\pi$
$984$	23.2711	+	40.3068i	0.741856	+	1.28493i
$985$	−4.32965	+	7.49917i	−0.137954	+	0.238943i
$986$	7.78198	+	13.4788i	0.247829	+	0.429252i
$987$		0			0
$988$	20.2661	−	24.4576i	0.644750	−	0.778101i
$989$	0.916066	+	1.58667i	0.0291292	+	0.0504533i
$990$	−6.17154			−0.196145
$991$	−27.6349			−0.877851			−0.438926	−	0.898523i	$-0.644641\pi$
$991$	−27.6349			−0.877851			−0.438926	+	0.898523i	$0.644641\pi$
$992$	−12.8762			−0.408819
$993$	48.2703			1.53181
$994$		0			0
$995$	−3.14227	+	5.44257i	−0.0996166	+	0.172541i
$996$	−2.45700	−	4.25565i	−0.0778531	−	0.134845i
$997$	1.01392	+	1.75615i	0.0321110	+	0.0556180i	0.881634	−	0.471933i	$-0.156444\pi$
$997$	1.01392	+	1.75615i	0.0321110	+	0.0556180i	−0.849523	+	0.527551i	$0.823110\pi$
$998$	12.7959			0.405047
$999$	−1.24535	+	2.15701i	−0.0394012	+	0.0682449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.k.263.3		8
7.2	even	3		637.2.h.h.471.2		8
7.3	odd	6		637.2.f.i.393.3		8
7.4	even	3		91.2.f.c.29.3	yes	8
7.5	odd	6		637.2.h.i.471.2		8
7.6	odd	2		637.2.g.j.263.3		8
13.9	even	3		637.2.h.h.165.2		8
21.11	odd	6		819.2.o.h.757.2		8
28.11	odd	6		1456.2.s.q.1121.4		8
91.3	odd	6		8281.2.a.bp.1.2		4
91.9	even	3	inner	637.2.g.k.373.3		8
91.10	odd	6		8281.2.a.bt.1.3		4
91.11	odd	12		1183.2.c.g.337.3		8
91.48	odd	6		637.2.h.i.165.2		8
91.61	odd	6		637.2.g.j.373.3		8
91.67	odd	12		1183.2.c.g.337.6		8
91.74	even	3		91.2.f.c.22.3	✓	8
91.81	even	3		1183.2.a.k.1.2		4
91.87	odd	6		637.2.f.i.295.3		8
91.88	even	6		1183.2.a.l.1.3		4
273.74	odd	6		819.2.o.h.568.2		8
364.347	odd	6		1456.2.s.q.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	91.74	even	3
91.2.f.c.29.3	yes	8	7.4	even	3
637.2.f.i.295.3		8	91.87	odd	6
637.2.f.i.393.3		8	7.3	odd	6
637.2.g.j.263.3		8	7.6	odd	2
637.2.g.j.373.3		8	91.61	odd	6
637.2.g.k.263.3		8	1.1	even	1	trivial
637.2.g.k.373.3		8	91.9	even	3	inner
637.2.h.h.165.2		8	13.9	even	3
637.2.h.h.471.2		8	7.2	even	3
637.2.h.i.165.2		8	91.48	odd	6
637.2.h.i.471.2		8	7.5	odd	6
819.2.o.h.568.2		8	273.74	odd	6
819.2.o.h.757.2		8	21.11	odd	6
1183.2.a.k.1.2		4	91.81	even	3
1183.2.a.l.1.3		4	91.88	even	6
1183.2.c.g.337.3		8	91.11	odd	12
1183.2.c.g.337.6		8	91.67	odd	12
1456.2.s.q.113.4		8	364.347	odd	6
1456.2.s.q.1121.4		8	28.11	odd	6
8281.2.a.bp.1.2		4	91.3	odd	6
8281.2.a.bt.1.3		4	91.10	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.355143 - 0.615126i) q^{2} +2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(0.644857 + 1.11692i) q^{5} +(0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +O(q^{10})\)	\(q+(0.355143 - 0.615126i) q^{2} +2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(0.644857 + 1.11692i) q^{5} +(0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +0.916066 q^{10} -2.40788 q^{11} +(1.80049 + 3.11853i) q^{12} +(1.25409 + 3.38042i) q^{13} +(1.55274 + 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(-1.95169 - 3.38042i) q^{17} +(0.993655 - 1.72106i) q^{18} -5.89068 q^{19} +(-0.964379 + 1.67035i) q^{20} +(-0.855143 + 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} +5.97829 q^{24} +(1.66832 - 2.88961i) q^{25} +(2.52477 + 0.429109i) q^{26} -0.486640 q^{27} +(-2.80683 - 4.86157i) q^{29} +2.20578 q^{30} +(-1.10289 + 1.91026i) q^{31} +(2.91873 + 5.05540i) q^{32} -5.79790 q^{33} -2.77252 q^{34} +(2.09212 + 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} +(-2.09204 + 3.62351i) q^{38} +(3.01971 + 8.13966i) q^{39} +(1.60105 + 2.77310i) q^{40} +(3.89260 + 6.74219i) q^{41} +(-0.144857 + 0.250899i) q^{43} +(-1.80049 - 3.11853i) q^{44} +(1.80424 + 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} +(-0.638511 - 1.10593i) q^{47} +(-1.47782 + 2.55966i) q^{48} +(-1.18499 - 2.05245i) q^{50} +(-4.69943 - 8.13966i) q^{51} +(-3.44036 + 4.15192i) q^{52} +(6.81126 - 11.7974i) q^{53} +(-0.172827 + 0.299345i) q^{54} +(-1.55274 - 2.68942i) q^{55} -14.1841 q^{57} -3.98731 q^{58} +(2.01528 + 3.49057i) q^{59} +(-2.32211 + 4.02201i) q^{60} -4.60097 q^{61} +(0.783368 + 1.35683i) q^{62} +1.69131 q^{64} +(-2.96697 + 3.58061i) q^{65} +(-2.05908 + 3.56644i) q^{66} +7.57559 q^{67} +(2.91873 - 5.05540i) q^{68} +(7.61366 - 13.1872i) q^{69} +(-3.61366 + 6.25905i) q^{71} +6.94662 q^{72} +(7.50626 - 13.0012i) q^{73} +(-1.81768 - 3.14832i) q^{74} +(4.01712 - 6.95785i) q^{75} +(-4.40474 - 7.62923i) q^{76} +(6.07935 + 1.03324i) q^{78} +(4.65379 + 8.06060i) q^{79} -1.58310 q^{80} -9.56546 q^{81} +5.52973 q^{82} -1.36463 q^{83} +(2.51712 - 4.35978i) q^{85} +(0.102890 + 0.178210i) q^{86} +(-6.75852 - 11.7061i) q^{87} -5.97829 q^{88} +(0.449849 - 0.779162i) q^{89} +2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} -0.907052 q^{94} +(-3.79865 - 6.57945i) q^{95} +(7.02797 + 12.1728i) q^{96} +(-7.83288 + 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9	\( 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9} - 22 q^{10} - 2 q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} - 19 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{22} + 2 q^{23} - 6 q^{24} - 5 q^{25} + 3 q^{26} - 52 q^{27} - q^{29} - 8 q^{30} + 4 q^{31} + 33 q^{32} - 38 q^{33} + 6 q^{34} + 34 q^{36} + 10 q^{37} + 23 q^{38} - 19 q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 34 q^{52} - 2 q^{53} - 5 q^{54} + 3 q^{55} - 34 q^{57} - 22 q^{58} + 8 q^{59} + 11 q^{60} + 16 q^{61} + 5 q^{62} + 28 q^{64} + 4 q^{65} - 6 q^{66} - 12 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} + 10 q^{72} + 8 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} + 14 q^{80} + 48 q^{81} - 28 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 6 q^{88} + q^{89} + 52 q^{90} + 24 q^{92} + 7 q^{93} + 66 q^{94} - 21 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9 - 22 * q^10 - 2 * q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 - 19 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 2 * q^20 - 5 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 + 3 * q^26 - 52 * q^27 - q^29 - 8 * q^30 + 4 * q^31 + 33 * q^32 - 38 * q^33 + 6 * q^34 + 34 * q^36 + 10 * q^37 + 23 * q^38 - 19 * q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 34 * q^52 - 2 * q^53 - 5 * q^54 + 3 * q^55 - 34 * q^57 - 22 * q^58 + 8 * q^59 + 11 * q^60 + 16 * q^61 + 5 * q^62 + 28 * q^64 + 4 * q^65 - 6 * q^66 - 12 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 + 10 * q^72 + 8 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 - q^78 + 26 * q^79 + 14 * q^80 + 48 * q^81 - 28 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 6 * q^88 + q^89 + 52 * q^90 + 24 * q^92 + 7 * q^93 + 66 * q^94 - 21 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more